Question

How do you solve `(6x)/(x+4)+4=(2x+2)/(x-1)`?

Answer 1

The solution for this equation is `x =2,-3/2`

Explanation:

`(6x)/(x+4)+4=(2x+2)/(x-1)`

or, `(6x+4*(x+4))/(x+4)=(2x+2)/(x-1) rarr` Take LCM on LHS.

or, `(6x+4x+16)/(x+4)=(2x+2)/(x-1)`

or, `(10x+16)/(x+4)=(2x+2)/(x-1)`

or, `(x-1)(10x+16)=(x+4)(2x+2) rarr` Cross Multiply

or, `x(10x+16)-1(10x+16)=x(2x+2)+4(2x+2) rarr`Simplify

or, `10x^2+16x-10x-16=2x^2+2x+8x+8rarr`Simplify

or, `10x^2+6x-16=2x^2+10x+8`

or, `2(5x^2+3x-8)=2(x^2+5x+4)rarr`Take 2 Common on both LHS Side and RHS Side

or, `(2(5x^2+3x-8))/2=(2(x^2+5x+4))/2rarr`Dividing both sides by 2

or, `5x^2+3x-8=x^2+5x+4`

or, `5x^2-x^2+3x-3x-8=x^2-x^2+5x-3x+4rarr`Subracting `x^2` and 3x from boths sides

or, `4x^2-8=2x+4`

or, `4x^2-8-4=2x+4-4rarr`Subtracting 4 from both sides

or, `4x^2-12=2x`

or, `4x^2-2x-12=2x-2xrarr` Subtracting 2x from both sides

or, `4x^2-2x-12=0`

or, `4x^2-8x+6x-12=0rarr` Factoring LHS

or, `4x(x-2)+6(x-2)=0`

or, `(4x+6)(x-2)=0`

Either 4x+6=0
or, `4x=-6`

or, `x=-(6/4)`

or, `x=-(3/2)`

Or,

`x-2=0`

or, `x=2`

:.The solution for `x=2,-3/2`.